Adding Fractions Calculator
The Adding Fractions Calculator adds two fractions and returns the sum as a fraction reduced to its lowest terms, along with the decimal value. Enter the numerator and denominator of each fraction and it finds a common denominator, adds the parts, and simplifies the answer for you.
Formula
a/b + c/d = (a×d + c×b) / (b×d), then reduced
- The two fractions are placed over a common denominator (b × d), the numerators are added, and the result is reduced by dividing both parts by their greatest common divisor.
- Formula: a/b + c/d = (a×d + c×b) / (b×d).
- Negative numerators are allowed; the sign is moved to the numerator in the final answer.
- Denominators must not be zero.
Example Calculation
Inputs
- First fraction — numerator: 1
- First fraction — denominator: 2
- Second fraction — numerator: 1
- Second fraction — denominator: 3
Add 1/2 and 1/3: a common denominator is 6, giving 3/6 + 2/6 = 5/6, or about 0.8333.
Frequently asked questions
How do you add two fractions?
Put both fractions over a common denominator, add the numerators, then reduce the result. This calculator does all three steps for you.
Does it simplify the answer?
Yes. The sum is reduced to lowest terms by dividing the numerator and denominator by their greatest common divisor.
Can I add negative fractions?
Yes. Enter a negative numerator and the calculator handles the sign correctly.
What if my denominators are different?
That is exactly what the calculator is for — it automatically finds a common denominator before adding.
Why can't a denominator be zero?
A fraction with a denominator of zero is undefined, so the calculator asks you to enter a non-zero denominator.